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Algorithms for Classical Orthogonal Polynomials
, 1996
"... In this article explicit formulas for the recurrence equation pn+1 (x) = (An x +Bn ) pn (x) \Gamma Cn pn\Gamma1 (x) and the derivative rules oe(x) p 0 n (x) = ff n pn+1 (x) + fi n pn (x) + fl n pn\Gamma1 (x) and oe(x) p 0 n (x) = (~ff n x + ~ fi n ) pn (x) + ~ fl n pn\Gamma1 (x) respectively ..."
Abstract

Cited by 8 (4 self)
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In this article explicit formulas for the recurrence equation pn+1 (x) = (An x +Bn ) pn (x) \Gamma Cn pn\Gamma1 (x) and the derivative rules oe(x) p 0 n (x) = ff n pn+1 (x) + fi n pn (x) + fl n pn\Gamma1 (x) and oe(x) p 0 n (x) = (~ff n x + ~ fi n ) pn (x) + ~ fl n pn\Gamma1 (x) respectively
Higher Order Turán Inequalities
"... The celebrated Tur'an inequalities P 2 n (x) \Gamma Pn\Gamma1 (x)Pn+1 (x) 0; x 2 [\Gamma1; 1]; n 1, where Pn (x) denotes the Legendre polynomial of degree n, are extended to inequalities for sums of products of four classical orthogonal polynomials. The proof is based on an extension of th ..."
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Cited by 6 (2 self)
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The celebrated Tur'an inequalities P 2 n (x) \Gamma Pn\Gamma1 (x)Pn+1 (x) 0; x 2 [\Gamma1; 1]; n 1, where Pn (x) denotes the Legendre polynomial of degree n, are extended to inequalities for sums of products of four classical orthogonal polynomials. The proof is based on an extension
Fast Discrete Polynomial Transforms with Applications to Data Analysis for Distance Transitive Graphs
, 1997
"... . Let P = fP 0 ; : : : ; Pn\Gamma1 g denote a set of polynomials with complex coefficients. Let Z = fz 0 ; : : : ; z n\Gamma1 g ae C denote any set of sample points. For any f = (f 0 ; : : : ; fn\Gamma1 ) 2 C n the discrete polynomial transform of f (with respect to P and Z) is defined as the col ..."
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Cited by 47 (9 self)
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. Let P = fP 0 ; : : : ; Pn\Gamma1 g denote a set of polynomials with complex coefficients. Let Z = fz 0 ; : : : ; z n\Gamma1 g ae C denote any set of sample points. For any f = (f 0 ; : : : ; fn\Gamma1 ) 2 C n the discrete polynomial transform of f (with respect to P and Z) is defined
The Hopf ring for P(n)
, 1995
"... We show that E (P (n) ), the Ehomology of the \Omega\Gammae/ ectrum for P (n), is an E free Hopf ring for E a complex oriented theory with I n sent to 0. This covers the cases P (q) (P (n) ) and K(q) (P (n) ), q n. The generators of the Hopf ring are those necessary for the stable ..."
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module spectrum obtained by killing the ideal I n = (p; v 1 ; v 2 ; \Delta \Delta \Delta v n\Gamma1 ) ae ß (BP ) via the SullivanBaas construction, [Baa73], [BM71], and [JW75]. For odd primes it is a nice multiplicative spectrum by [Mor79], [SY76], and [Wur77]. Partially supported by the National Science
Photos monte carlo: A precision tool for qed corrections in z and w decays, Eur
 Phys. J. C45
"... We present a discussion of the precision for the PHOTOS Monte Carlo algorithm, with improved implementation of QED interference and multiplephoton radiation. The main application of PHOTOS is the generation of QED radiative corrections in decays of any resonances, simulated by a “host ” Monte Carlo ..."
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Cited by 185 (0 self)
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Carlo generator. By careful comparisons automated with the help of the MCTESTER tool specially tailored for that purpose, we found that the precision of the current version of PHOTOS is of 0.1 % in the case of Z and W decays. In the general case, the precision of PHOTOS was also improved
qDistributions and Markov Processes
, 1996
"... We consider a sequence of integervalued random variables Xn ; n 1; representing a special Markov process with transition probability n;` , satisfying P n;` = (1\Gamma n;` ) Pn\Gamma1;` + n;`\Gamma1 Pn\Gamma1;`\Gamma1 : Whenever the transition probability is given by n;` = q ff n+fi `+fl and ..."
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Cited by 4 (0 self)
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We consider a sequence of integervalued random variables Xn ; n 1; representing a special Markov process with transition probability n;` , satisfying P n;` = (1\Gamma n;` ) Pn\Gamma1;` + n;`\Gamma1 Pn\Gamma1;`\Gamma1 : Whenever the transition probability is given by n;` = q ff n+fi `+fl
The classical Jacobi Polynomials Pn
"... We observe that the exact connection coefficient relations transforming modal coefficients of one Jacobi Polynomial class to the modal coefficients of certain other classes are sparse. Because of this, when one of the classes corresponds to the Chebyshev case, the Fast Fourier Transform can be used ..."
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We observe that the exact connection coefficient relations transforming modal coefficients of one Jacobi Polynomial class to the modal coefficients of certain other classes are sparse. Because of this, when one of the classes corresponds to the Chebyshev case, the Fast Fourier Transform can be used to quickly compute modal coefficients for Jacobi Polynomial expansions of class (α, β) when 2α and 2β are both odd integers. In addition, we present an algorithm for computing Jacobi spectral expansions that is more robust than JacobiGauss quadrature. Numerical results are presented that illustrate the computational efficiency and accuracy advantage of our method over standard quadrature methods.
Results 1  10
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44,009